Question: Solve for $x$ and $y$ using elimination. ${-5x-2y = -58}$ ${3x+3y = 51}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $2$ ${-15x-6y = -174}$ $6x+6y = 102$ Add the top and bottom equations together. $-9x = -72$ $\dfrac{-9x}{{-9}} = \dfrac{-72}{{-9}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {-5x-2y = -58}\thinspace$ to find $y$ ${-5}{(8)}{ - 2y = -58}$ $-40-2y = -58$ $-40{+40} - 2y = -58{+40}$ $-2y = -18$ $\dfrac{-2y}{{-2}} = \dfrac{-18}{{-2}}$ ${y = 9}$ You can also plug ${x = 8}$ into $\thinspace {3x+3y = 51}\thinspace$ and get the same answer for $y$ : ${3}{(8)}{ + 3y = 51}$ ${y = 9}$